Here, we consider the microscopic tight binding models with the inter-layer hopping depending only on the hopping displacement, as in Ref. [1]}. We introduce the notation for the Fourier transformation of the hopping
\( \tilde{t}_{d_0}(q) = A_{mlg}^{-1} \int {\rm d}^2 y\ e^{- i q \cdot y} t(y + d_0 \hat{z}) \quad \Longrightarrow \quad A_{mlg}^{-1} \int {\rm d}^2 y\ e^{- i q \cdot y} y t(y + d_0 \hat{z}) = i \nabla _{q} \tilde{t}_{d_0}(q) \) 
